External structure of crystals

Dr. Ahmad Redaa

2024-09-11

Introduction

  1. Definition of a Crystal and Crystallization
  2. Crystal Elements:
    • Crystal Faces
    • Edges
    • Solid Angles
    • Interfacial Angles
  3. Elements of Symmetry:
    • Axes of Symmetry
    • Plane of Symmetry
    • Centre of Symmetry
  4. Miller Indices
  5. Law of Symmetry
  6. Crystallographic Systems:
    • Cubic System
    • Tetragonal System
    • Hexagonal System
    • Trigonal System
    • Orthorhombic System
    • Monoclinic System
    • Triclinic System

Definition of a Crystal and Crystallization

Crystal Elements

Crystal Elements of a cube

Crystallographic Axes

Crystallographic Axes and Their Names

Angles Between the Crystallographic Axes

Importance of Crystallographic Axes

Crystallographic Systems and Their Axes

  1. Cubic: a = b = c; α = β = γ = 90°
  2. Tetragonal: a = b ≠ c; α = β = γ = 90°
  3. Orthorhombic: a ≠ b ≠ c; α = β = γ = 90°
  4. Hexagonal: a = b ≠ c; α = β = 90°, γ = 120°
  5. Trigonal: a = b = c; α = β = γ ≠ 90°
  6. Monoclinic: a ≠ b ≠ c; α = γ = 90°, β ≠ 90°
  7. Triclinic: a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90°

Crystallographic Axes, Source: https://www.tulane.edu/

Elements of Symmetry

Axes of Symmetry, Source: https://www.mindat.org

Plane of Symmetry, Source: https://www.mindat.org

Centre of Symmetry, Source: https://www.mindat.org

Law of Symmetry

Hermann-Mauguin (International) Symbols

Hermann-Mauguin (International) Symbol of Rhombic-dipyramidal, Source: https://www.tulane.edu/

Miller Indices

Determining Miller Indices of various planes in the cubic lattice , Source: https://www.physics.rutgers.edu/